Blackjack games are extremely popular and well-known card games. Typically, a Blackjack game is associated with one or more standard decks of fifty-two playing cards. Each numbered card has a value that is equal to its face value; each Jack, Queen, and King has a value of ten; and each Ace has a value of either one or eleven, depending on which value is more beneficial. The dealer begins a play of the Blackjack game by dealing a hand of two cards to each player who has placed a wager. The dealer also deals a hand of two cards to himself or herself. One of the cards of the dealer's hand is dealt face up (called the “up card”) and the other card of the dealer's hand is dealt face down (called the “down card”). Each hand has a count, which is equal to a sum of the values of the cards of that hand.
A player may draw one or more additional cards to add to the player's hand to increase the count of the player's hand. This is referred to as “hitting.” If the count of the player's hand exceeds twenty-one following a “hit,” however, then the player “busts,” Once the player “busts,” the player loses and the player's wager is forfeited regardless of whether the dealer “busts.” The player can “stand” rather than “hit” when the count of the player's hand is twenty-one or less. In other words, “hitting” is optional for the player.
Each gaming establishment has house rules that govern how the Blackjack game is to be played and, in particular, when the dealer must “hit.” House rules can vary from establishment to establishment or Blackjack game to Blackjack game. Usually, the dealer must “hit” when the count of the dealer's hand is less than seventeen. Some house rules require that a dealer “hit” when the dealer's hand includes an Ace and a Six (or an Ace and multiple additional cards having values adding up to six), known as a “soft” seventeen (because an Ace can have the value of either eleven or one). Normally, a dealer must “stand” on a “soft” eighteen, nineteen, or twenty.
If the dealer “busts,” each player wins, regardless of that player's hand, unless that player has “busted.” If the dealer does not “bust,” for each player who did not “bust,” that player wins if the count of that player's hand is closer to twenty-one than the count of the dealer's hand. That player loses if the count of the dealer's hand is closer to twenty-on than the count of that player's hand. If, however, the count of that player's hand and the count of the dealer's hand are equal, the play of the Blackjack game results in a “push,” and the player's wager is returned to the player.
“Doubling down” is an optional procedure of a player doubling the player's original wager after the player's initial two cards are dealt, and then drawing a single additional card to add to the player's hand. The three-card hand becomes the player's final hand. In many gaming establishments, the house rules restrict this option, often allowing it only if the values of the player's first two cards total ten or eleven.
“Splitting” is an optional procedure of splitting a pair of cards having the same value dealt to a player into two hands by making an additional wager equal to the original wager. Each of these wagers is applied to a different one of the split hands. The player receives a new second card for each of the split hands, and each split hand is then played out separately. When “splitting” Aces, the player can usually receive only one additional card for each split hand, depending on the house rules.
“Insurance” is an optional procedure that is available when the dealer's “up card” is an Ace. After each player receives that player's first two cards and the dealer reveals the dealer's “up card,” each player can wager one-half of the amount of that player's original wager as “insurance” against the dealer having a “Blackjack” (a two-card twenty-one count). If the dealer has a “Blackjack,” the player loses the player's original wager and wins 2-to-1 on the insurance wager. On the other hand, if the dealer does not have a “Blackjack,” the player loses the player's insurance wager and play continues with respect to the player's original wager.
“Surrender” is an optional procedure that varies according to house rules, but when allowed, permits a player to forfeit one-half of the player's wager after the player's first two cards are dealt and evaluated against the dealer's “up card.”
In recent years, poker games have also become extremely popular. One common poker game is Pai Gow Poker. Pai Gow Poker is a variation of the Chinese domino game Pai Cow, and is played using playing cards rather than dominoes. Pai Gow Poker is typically played with a fifty-three card deck that includes fifty-two cards from a standard deck of playing cards and a single Joker. Pai Gow Poker is also typically played at a gaming table with a physical deck of cards and a live human dealer, though Pai Cow Poker can also be played on an electronic gaming machine (EGM) using electronic cards. Generally, in Pai Gow Poker, multiple players directly compete against a dealer. Each player attempts to form two high ranking hands from a set of seven initially dealt player cards.
More specifically, a round of play of the game begins after each of the players places an initial wager. Each player is dealt seven cards. After the cards have been dealt, each player views that player's cards and arranges that player's seven cards into a five-card player hand and a two-card player hand. For a player to win, both of the player's hands must beat both of the dealer's hands (as discussed below).
In Pai Gow Poker, a player's five-card hand is evaluated similarly to how five-card hands are evaluated in a standard game of Five Card Draw Poker, with a few exceptions discussed below. For the player's five-card hand, there are ten general categories or ranks of hands, ranked from highest to lowest, as shown in Table 1 below.
TABLE 1Ranking of Five-card Poker Hands by CategoryRankHand TypeExample1Royal Straight FlushA   K   Q   J   10  2Straight FlushK   Q   J   10   9  3Four-of-a-KindJ   J♥ J♦ J   3  4Full HouseA♥ A♦ A   6♦ 6  5FlushA   J   8   6   2  6Straight8♦ 7   6   5   4  7Three-of-a-KindQ   Q♥ Q♦ 6♦ 2  8Two Pair8♦ 8♥ 5♥ 5   2  9One PairK♦ K   8   7   2♥10High CardA♥ 10   7♦ 5   3  
When comparing two five-card hands, the hand with the higher-ranking hand type wins. When the two hands have the same hand type, the stronger hand is determined relative to the card ranks making up each hand, with an Ace being the highest card and a Two being the lowest card. There is no difference in rank between the four card suits. All hands can be ranked in a linear ranking from highest to lowest. Because suits are all of the same value, however, there are multiple hands that have identical rankings. For example, a Straight Flush including 5 6 7 8 9 is equivalent to a straight flush of all the same ranks but of a different suit, such as 5♥ 6♥ 7♥ 8♥ 9♥.
For the One Pair, Three-of-a-Kind, and Four-of-a-Kind outcomes, the hand with the highest matching rank wins. For example, a Pair of Kings beats a Pair of Tens.
For a Two Pair outcome, the hand with the higher high Pair wins. For example, a hand including 3-3-8-8 beats a hand including 5-5-7-7, since the high Pair of Eights beats the high Pair of Sevens. If the high Pair is the same, then the low Pair is compared. For example, a hand including 5-5-J-J beats a hand including 3-3-J-J because the high Pair matches and the low Pair of Fives beats the low Pair of Threes.
For a Full House, the hand with the higher Three-of-a-Kind wins. For example, a hand including K-K-8-8-8 beats a hand including A-A-5-5-5 because the three Eights beat the three Fives.
When comparing Straight, Flush, or Straight Flush hands, the hand with the highest card rank wins. For example, a 7-8-9-10-J Straight beats a 6-7-8-9-10 Straight. In Pai Gow Poker, the highest Straight is a 10-J-Q-K-A. The second highest Straight is an A-2-3-4-5. The third highest straight is a 9-10-J-Q-K.
When comparing two Flush hands, the hand with the highest ranking card wins. If both hands have the same highest ranking card rank, then the next highest card ranks are compared. This is the same way that two High Card hands are compared.
If the winning outcomes are the same between two hands, then the remaining cards in the hand are examined. For example, a hand including 5-3-3-8-8 beats a hand including 4-3-3-8-8. While the high and low Pairs both match, the remaining Five beats the Four. Likewise, a hand including 4-9-J-8-8 beats a hand including 4-6-J-8-8. The Pair of Eights match, as do the high card Jacks. Looking at the next highest cards, however, the Nine beats the Six.
For the player's two-card hand, there are only two general categories or ranks of hands, ranked from highest to lowest, as shown in Table 1 below.
TABLE 2Ranking of Two-card Poker Hands by CategoryRank Hand TypeExample1One PairA   A♦2High CardK   9♥
Within each of the two categories, hands are ranked according to the rank of individual cards, with an Ace being the highest card and a Two being the lowest card. The highest ranking two-card Pai Cow Poker hand is a pair of Aces (A♥ A), and the lowest ranking hand includes a Two-Three combination (e.g., 2♦ 3).
In certain Pai Cow Poker games that include a Joker card, the Joker can only be used as a wild card to complete a Straight, a Flush, a Straight Flush, or a Royal Straight Flush. In the case of completing a Straight, a Flush or a Straight Flush, the Joker is assigned the highest rank possible within that context. For example, in the hand Joker Q J 10 9, the Joker is evaluated as being a K even though the Joker's evaluation as a 8 would also yield a Straight Flush. In a similar example, in the hand Joker A J 8 6, the Joker is evaluated as being the largest rank available, which for his example would be the K. If a Joker cannot be used to complete a Straight, a Flush, a Straight Flush, or a Royal Straight Flush, the Joker is given the value of an Ace.
After each of the players has arranged the player's seven cards into a five-card player hand and a two-card player hand, the dealer arranges the seven dealer cards into a five-card dealer hand and a two-card dealer hand according to a set of rules commonly known as “House Way” rules. The “House Way” rules can vary from one gaming establishment to another, as described further below. For each of the players, after the dealer has arranged the set of seven dealer cards to form the five-card dealer hand and the two-card dealer hand, the dealer compares the five-card player hand to the five-card dealer hand and the two-card player hand to the two-card dealer hand. If both of the five-card player hand and two-card player hand beat the respective dealer hands, then the player wins an award. Under certain Pai Cow Poker house rules, if the player wins, the house may take a defined percentage of the player's award (known as a commission, a vigorish, or a “vig”). If both the dealer five-card hand and two-card hand beat the respective player hands, the player loses and the player's wager is forfeited. If one of the player's hands beats its respective dealer hand and the other one of the player's hands loses to its respective dealer hand, the player “pushes” on the round of play of the game and the player's wager is returned. In Pai Cow Poker, this type of a tie (i.e., one winning hand and one losing hand) occurs fairly often. If the rank of the five-card player hand is the same as the rank of the five-card dealer hand and if the rank of the two-card player hand is the same as the rank of the two-card dealer hand, the player loses the wager. This type of a tie-tie situation is sometimes referred to as a copy.
In Psi Gow Poker, there are several rules or restrictions that dictate how a player must form the player's five-card and two-card player hands. For example, the two-card player hand must rank lower than the five-card player hand. For example, if both the two-card hand and the five-card hand are of the type One Pair, the two-card hand is not allowed to have a higher ranking pair than the five-card hand. Similarly, if both the two-card hand and the five-card hand are of the hand type High Card, the two-card hand is not allowed to have a higher ranking high card than the five-card hand. However, if the five-card hand is of the hand type Two Pair and the two-card hand is of the hand type One Pair, the pair in the two-card hand can be of a higher rank than either pair within the five-card hand because the five-card hand is of a higher ranking hand type. If a player mistakenly sets the two-card player hand to have a higher rank than the five-card player hand (e.g., a five-card hand having only a High Card ranking, such as A♥ K 9♥ 6 4♦, and a two-card hand having a Pair, such as Q♥ Q), then both hands are determined to be “foul.” When the game is offered on a physical table with a live dealer, certain gaming establishment rules will result in a “foul” hand automatically losing. When the game is offered on an EGM, the EGM typically warns the player of the attempt at setting a foul hand and prompts the player to correct the player's setting. In an EGM that supports multiplayer play, a time limit may be established. If a given player is unable to set the player's hand within an allotted period of Lime, the EGM will set the player's hand on the player's behalf according to the House Way rules.
In certain gaming establishments, a player may request that the dealer set the player's hand according to house way rules. When the game is offered at a physical table with a live dealer, the setting of a player hand is typically handled as follows. A player places the cards face down in a single stack and announces to the dealer the desire for the dealer to set that hand. After all other players at the table have set their own hands, the dealer will assist any players requesting house setting one at a time. For a given player, the dealer will reveal that player's cards, set the cards according to the House Way rules, and then place the cards in the areas that the player would normally do so himself or herself. Casinos typically use this order of operation to prevent players from seeing any cards other than their own before setting theft own hands, as casinos are concerned that an expert player may be able to achieve an advantage against the casino if the player is able to deduce what cards the dealer holds by a process of elimination regarding revealed player cards.
Under certain Pai Gow Poker gaming configurations, a player may elect to act as the banker. When a player plays the role of the banker, the player competes against the other player or players at the table. If the player who is playing the role of banker wins, the player-banker wins an award and a commission based on the winnings is paid to the house. Under certain game rules, when a player is acting the role of banker, the dealer still participates in the game. In general, the opportunity for player to play the role of banker rotates around the table. Alternatively, the opportunity to play the role of the banker may alternate between player and dealer between each round of play. As mentioned above, however, the players may alternatively elect to decline this option. If a player elects to play the role of the banker, the player must have enough money to pay losses to the other players and the dealer assuming that the player/banker loses to all of the other players and the dealer.
One factor in determining a player's odds of beating the dealer (or other player-banker) is based upon the way in which a player arranges the player's cards to form the five-card player hand and the two-card player hand. That is, there are many ways that a player could set the player's cards without having “foul” hands, but there are card setting strategies that can optimize the player's probability of beating the dealer. In certain known Pai Gow Poker games, whether the games are operated on an EGM or dealt by a live human dealer, the games include the following characteristics: (a) the cards in the dealer hand are set according to a set of “House Way” rules, and (b) a player can either set their own cards according to the rules of the game or can request to have the dealer set the cards in the player's hand according to the “House Way” rules. In general, the “House Way” rules are not the same as optimal play rules, “House Way” rules are generally simplified rules relative to optimal play rules because the simplified rules are not overly complex and enable a human dealer to learn, remember, and execute simple rules to reduce the chance of dealer errors and to reduce the chance of player disputes.
The “House Way” rules can differ based on the preferences of the gaming establishment, local gaming regulations, regional customer preferences, and/or other factors. One example of a set of “House Way” rules for setting the dealer hands is outlined below. As mentioned above, the dealer receives seven cards and must divide the seven cards into a five-card dealer hand and a two-card dealer hand, where the five-card dealer hand must have a higher rank than the two-card dealer hand.
Under this example set of “House Way” rules, if the seven dealer cards do not include a pair (e.g., A♥, K, J, 8♥, 6, 4♦, and 3), the dealer must place the highest value card (A♥) in the five-card dealer hand and must place the next two highest cards (K J) in the two-card dealer hand. A hand such as this, whether it be a player hand or a dealer hand, that does not include a pair or better is often referred to as a “Pai Cow.” By placing the highest value card in the five-card dealer hand, the hands are not “foul.” Moreover, even assuming that the dealer will lose the five-card dealer hand, placing the next two highest cards in the two-card dealer hand will maximize the probability that the dealer will win at least one of the two hands and tie the player(s) (i.e., a “push” outcome). Certain “House Way” rules are configured to maximize the probability that the dealer will tie the player (i.e., that the dealer will have one winning hand and one losing hand).
If the seven dealer cards include one pair (e.g., A, K, J, J♥, 6, 4♦, and 3), the dealer must place the pair (J J♥) in the five-card dealer hand and the next two highest value cards (A K) in the two-card dealer hand. In this example rule, the Ace and the King are more useful in the two-card dealer hand, and would not significantly affect or improve the rank of the five-card dealer hand.
If the seven dealer cards include two pairs, the dealer must place both of the pairs in the five-card dealer hand except in the following circumstances:                (a) if one of the pairs is Sevens or greater and there are no singleton Aces (i.e., a non-paired Ace), then place the higher pair in the five-card dealer hand and the lower pair in the two-card dealer hand;        (b) if one of the pairs is Jacks or better, if the other of the pairs is Sixes or better, and there is a singleton Ace, then place the higher pair in the five-card dealer hand and the lower pair in the two-card dealer hand; and        (c) if one of the pairs is a pair of Aces, then place the pair of Aces in the five-card dealer hand and the lower pair in the two-card dealer hand. In this case, because the pair of Aces is already a high pair (and relatively high ranking five-card hand) the benefit of placing the lower pair in the two-card dealer hand exceeds the detriment of sacrificing a Two Pair hand as the five-card dealer hand.        
If the seven dealer cards include three pairs (e.g., A♥, A, 10♥, 10, 6, 6♦, and J♥) always place the highest ranking pair (A♥ A) in the two-card dealer hand and place the remaining two pair (10♥ 10 and 6 6♦) in the five-card dealer hand.
If the seven dealer cards include a Three-of-a-Kind, the dealer must place the Three-of-a-Kind in the five-card dealer hand unless the Three-of-a-Kind includes three Aces. If the Three-of-a-Kind includes Aces, place a pair of Aces in the five-card dealer hand, and place the third Ace in the two-card dealer hand.
If the seven dealer cards include a Full House (e.g., K, K♦, K, 4♦, 4, 9♦ and 7), the dealer must split the Rill House into a Three-of-a-Kind (K, K♦, K) and a pair (4♦, 4) with the Three-of-a-Kind being placed in the five-card dealer hand. This rule has the following exceptions:                (a) if the Full House include a pair of Twos, the Full House does not need to be split up; and        (b) if the remaining two-cards of the seven dealer cards are an Ace and a King, the Full House does not need to be split up.        
If the seven dealer cards include a Full House with a Three-of-a-Kind and two pairs (e.g., K, K♦, K, 4♦, 4, 9♦, and 9), the dealer must place the higher of the two pairs (i.e., 9▴ 9) in the two-card dealer hand. In this example hand, a Full House is likely to beat most five-card player hands. Therefore, the marginal benefit of having a higher pair in the five-card dealer hand is less than the marginal benefit of having a higher pair in the two-card dealer hand. In a single deck game having only four Kings, it would not be possible for another player to be dealt three Kings because the deck includes only one remaining King. Therefore, because no other player could be dealt a Full House including three Kings, there is no marginal benefit to having a higher second pair in the five-card dealer hand.
If the seven dealer cards include two separate Three-of-a-Kinds (e.g., J♥, J♦, J, 2♥, 2, 2, 6♦), the higher ranking of the two Three-of-a-Kinds (i.e., J♥, J♦, J) should be split up and the pair of Jacks should be placed in the two-card dealer hand. In the example above, the final five-card dealer hand would include 2♥ 2 2 J♥ 6♦, and the final two-card dealer hand would include J♦ J. Because a Three-of-a-Kind is a relatively high ranking hand, the marginal benefit of having a higher ranking pair (e.g., J♥ J♦ instead of 2♥ 2) is greater than the marginal benefit of having a higher valued Three-of-a-Kind. Moreover, the marginal benefit of forming a Full House in the five-card dealer hand (e.g., J♥, J▴ J2) is not high enough to forego forming a pair in the two-card dealer hand.
If the seven dealer cards include a Straight, a Flush, a Straight Flush, or a Royal Straight Flush, the dealer uses these five cards in the five-card dealer hand except in the following circumstances in which the seven dealer cards also include two pairs:                (a) if the seven dealer cards include an Ace singleton (e.g., the following hand includes Two Pair, a Hearts Flush, and an Ace singleton: A♥ K♥ K♦ 10♥ 10 9♥ 3♥);        (b) if the seven dealer cards include a pair of Jacks and a pair of Sixes (e.g., A♥ J♥ J▴ 6♥ 6 9♥ 3♥); and        (c) if the seven dealer cards include a pair of Aces and any other pair (A♥ A♦ K♥ 10♥ 8♥ 3♦ 3♥.        
If the seven dealer cards include a six or seven card Straight or Flush (e.g., K♥ Q♥ J▴ 4 9 8♥ 7♥), form the highest possible two-card dealer hand (K♥ Q♥) while maintaining the Straight or Flush in the five-card dealer hand (J♦ 10 9 8♥ 7♥). If the seven dealer cards include a Straight Flush (e.g., J♥ 10♥ 9♥ 8♥ 7♥ 4♥ 2), form only a Straight or Flush in the five-card dealer hand if the two-card dealer hand can be made to include a Jack or higher. In the example above, the five-card dealer hand should be set to include a Flush (10♥ 9♥ 8♥ 7♥ 4♥), and the two-card dealer hand should be set to include the J♥ and 2. If the seven dealer cards include a Royal Straight Flush (e.g., A♥ K♥ A♥ J♥ 10♥ 6♥ 2), form only a Straight or Flush in the five-card dealer hand if the two-card dealer hand can be made to include an Ace or higher. In the example above, the five-card dealer hand should be set to include a Flush (K♥ Q♥ J♥ 10♥ 6♥), and the two-card dealer hand should be set to include the A♥ and 2.
If the seven dealer cards include a Four-of-a-Kind, whether to split the Four-of-a-Kind into two separate pairs is determined according to the rank of the Four-of-a-Kind as follows:                (a) if the rank is a Two through Six (e.g., 4♥ 4♦ 4 4 J♥ 10 2♥), always keep the Four-of-a-Kind together;        (b) if the rank is Seven through Ten, split the Four-of-a-Kind into two pairs unless an Ace or better can be played in the two-card dealer hand;        (c) if the rank is a Jack through King, split the Four-of-a-Kind into two pairs unless the hand also includes a pair of Tens or higher (e.g., the Four-of-a-Kind in the following hand should not be split: J♥ J♦ J J 10♥ 10 2♥); and        (d) if the rank is Aces, split unless the seven dealer cards also include a pair of Sevens or higher (e.g., the Four-of-a-Kind in the following hand should not be split: A♥ A♦ A A 7♥ 7 2♥).        
Finally, if the seven dealer cards include five Aces, split the five Aces up (i.e., three Aces in the five-card dealer hand and two Aces in the two-card dealer hand) unless a pair of Kings can be played in the two-card dealer hand (e.g., the five Aces in the following hand should not be split: A♥ A♦ A A A♥ K K♥).
As mentioned above, although the above example of “House Way” rules has been explained, the “House Way” rules can differ from gaming establishment to gaming establishment. For instance, in a second example of “House Way” rules, the rules for splitting Two Pair differ slightly from the first example of “House Way” rules described above. In this second example set of “House Way” rules, if the seven dealer cards include Two Pair, the pairs are split except in the following situations:                (a) if both of the pairs are of a rank of six or less;        (b) if both of the pairs are of a rank of ten or less and there is an Ace singleton; and        (c) if one pair is a rank of Jack or greater, one pair is a rank of five or less, and there is an Ace singleton.        
Certain players seek out variations to card games such as Blackjack and Pai Gow Poker. A continuing need thus exists for gaming systems and methods that provide new, exciting, and engaging card games.